Controlled Markov Chains

Time-Sharing Policies for Controlled Markov Chains

We propose a class of non-stationary policies called \policy time sharing" (p.t.s.), which possess several desirable properties for problems where the criteria are of the average-cost type; an optimal policy exists within this class, the computation of optimal policies is straightforward, and the implementation of this policy is easy. While in the nite state case stationary policies are also kn...

Controlled Markov Chains, Graphs, and Hamiltonicity

This manuscript summarizes a line of research that maps certain classical problems of discrete mathematics — such as the Hamiltonian Cycle and the Traveling Salesman Problems — into convex domains where continuum analysis can be carried out. Arguably, the inherent difficulty of these, now classical, problems stems precisely from the discrete nature of domains in which these problems are posed. ...

Controlled Markov chains with safety upper bound

In this paper we introduce and study the notion of safety control of stochastic discrete event systems (DESs), modeled as controlled Markov chains. For non-stochastic DESs, modeled by state machines or automata, safety is specified as a set of forbidden states, or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited. We generalize this ...

Controlled Markov Chains and Safety Criteria

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...